A decomposition theorem for binary Markov random fields
type: Item
instance of: scholarly article
title: A decomposition theorem for binary Markov random fields
zbMATH Open document ID: 0626.60045
author: Bruce Hajek
author: Toby Berger
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: Consider a binary Markov random field whose neighbor structure is specified by a countable graph with nodes of uniformly bounded degree. Under a minimal assumption we prove a decomposition theorem to the effect that such a Markov random field can be represented as the nodewise modulo 2 sum of two independent binary random fields, one of which is white binary noise of positive weight. Said decomposition provides the information theorist with an exact expression for the per-site rate-distortion function of the random field over an interval of distortions not exceeding this weight. We mention possible implications for communication theory, probability theory and statistical physics.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 94A34
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4018024
zbMATH Keywords: Gibbs random field
zbMATH Keywords: Ising model
zbMATH Keywords: rate-distortion function
zbMATH Keywords: Markov random field
zbMATH Keywords: communication theory
zbMATH Keywords: statistical physics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992084
OpenAlex ID: W2013523725
DOI: 10.1214/AOP/1176992084
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description: scientific article; zbMATH DE number 4018024